Finite element methods for parameter identification problem of linear and nonlinear steady-state diffusion equations

We study a parameter identification problem for the steady state diffusion equations. In this thesis, we transform this identification problem into a minimization problem by considering an appropriate cost functional and propose a finite element method for the identification of the parameter for the linear and nonlinear partial differential equation. The cost functional involves the classical output least square term, a term approximating the derivative of the piezometric head 𝑢(𝑥), an equation error term plus some regularization terms, which happen to be a norm or a semi-norm of the variables in the cost functional in an appropriate Sobolev space. The existence and uniqueness of the minimizer for the cost functional is proved. Error estimates in a weighted 𝐻⁻¹-norm, 𝐿²-norm and 𝐿¹-norm for the numerical solution are derived. Numerical examples will be given to show features of this numerical method.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1997

Author dc:creator

• Ramirez, Edgardo II

Chair dc:contributor.committeechair

• Lin, Tao

Committee members dc:contributor.committeemember

• Burns, John A.
• Rogers, Robert C.
• Russell, David L.
• Sun, Shu-Ming

• Parameter identification
• Elliptic PDEs
• Finite Element Methods
• Optimization Algorithms

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-0698-13015

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28173